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<font size="6" color="Magenta">Dynamic Tip Clearance Library Block</font>
<br>
This block simulates the dynamic response of tip clearance inside turbomachinery. 
The block is capable of modeling a traditional tip clearance control system that is 
based on thermal management techniques. It models elastic axisymmetric deformation 
of the compressor/turbine structure (blade, rotor, and engine casing/shroud) due to thermal 
expansion and centrifugal forces. 
<p>The tip clearance is calculated based on the lengths of the relevant
structures.<p>
$$
TC = r_{in,Shroud} - \left[ r_{out,Rotor} + L_{Blade} \right] 
$$
where
$$
TC = tip \: clearance
$$
$$
r_{in,Shroud} = inner \: radius \: of \: the \: shroud
$$
$$
r_{out,Rotor} = outer \: radius \: of \: the \: rotor \: disc
$$
$$
L_{Blade} = length \: of \: the \: blade
$$
<p>The inner radius of the shroud is assumed to be offset from the inner surface of the
casing by a fixed distance. Since the casing provides the structural support for the 
shroud, its deformation is determined to obtain the displacement of the shroud.<p>
$$
r_{in,Shroud} = r_{in,Case} - L_{Shroud}
$$
The blade is treated as a lumped mass due to is small mass and relatively large surface 
area. The blade as assumed to be cooled through film cooling. The effective temperature 
of the gas on the blades surface which the blade temperature is approaching is given by 
the equation below.
$$
T_{ref} = T_{core,Blade} + \eta \left( T_{cool,Blade} - T_{core,Blade} \right)
$$
where
$$
T_{core,Blade} = temperature \: of \: the \: hot \: gas \: exposed \: to \: the \: blade
$$
$$
T_{cool,Blade} = temperature \: of \: the \: film \: cooling \: flow
$$
$$
\eta = film \: cooling \: coefficient
$$
The blade temperature governed by the following equation.
$$
\frac{dT_{Blade}}{dt} = \frac{h_{Blade} A_{Blade}}{Cp_{Blade} m_{Blade}} \left( T_{ref} - T_{Blade} \right)
$$
where
$$
T_{Blade} = temperature \: of \: the \: blade
$$
$$
m_{Blade} = mass \: of \: the \: blade
$$
$$
A_{Blade} = effective surface area \: of \: the \: blade
$$
$$
Cp_{Blade} = heat capacity \: of \: the \: blade
$$
$$
h_{Blade} = convective \: heat \: transfer \: coefficient \: between \: the \: blade \: and \: flow
$$
This approach is similar to function of the 0-D Trans Conduction model (Lumped Cap) 
block in T-MATS except it allows for temperature-varying and time-varying properties.<p>
The rotor disc and engine case utilize a 1-D finite difference approach which is performed by 
a 1-D Trans Conduction Model - Variable Props + Generic BCs block extracted from T-MATS.
The rotor disc is cooled on its front and back side using air bled off the engine. Similarly
cthe engine case is cooled on its inner and outer surface by air bled from the engine gas 
path. The location of the bleeds may differ depending on the design of the engine. The 
average temperatures of the components are used in a 1-D elastic thermal deformation model 
via a Thermal Expansion block that originated from T-MATS. Deformation of the rotor and blade 
due to centrifugal forces is based on equations derived for elastic mechanical deformation 
of simplified geometries. 
$$
u_{Blade} = \frac{1}{4 E_{Rotor}} \left(  1 - \nu_{Rotor} \right) \rho_{Rotor} \omega^2 r_{out,Rotor}^3
$$
$$
u_{Rotor} = \frac{1}{E_{Blade}} L_{Blade}^2 \left(  L_{Blade} + r_{out,Rotor} \right) \rho_{Blade} \omega^2
$$
where
$$
u = deflection \: from \: nominal \: length \: or \: radius \: without \: and \: centrifugal \: force
$$
$$
E = Young's \: Modulus
$$
$$
\nu = Poisson's \: ratio
$$
$$
\rho = Density
$$
$$
\omega = Shaft \: speed \: in \: rad/sec
$$
This block provides numerous options including options for modeling the convective heat 
transfer coefficients and addressing temperature dependence of properties such as thermal 
conductivity, heat capacity, thermal expansion coefficient, Young's Modulus, and Poisson's ratio.
The options for convective heat transfer models is to specify a constant convective heat 
transfer coefficient, use the model:
$$
h = h_{coeff} \left( \frac{T}{T_{des}} \right)^{0.23} \left( \frac{W}{W_{des}} \right)^{0.8}
$$
where
$$
h_{coeff} = the \: nominal \: heat \: transfer \: coefficient \: at \: the \: design/known \: data \: point \: \left( T_{des},W_{des} \right)
$$
$$
W = the \: temperature \: of \: the \: flow
$$
$$
T = the \: mass \: flow \: rate \: of \: the \: flow
$$
$$
W_{des} = the \: temperature \: of \: the \: flow \: at \: the \: design/known \: data \: point 
$$
$$
T_{des} = the \: mass \: flow \: rate \: of \: the \: flow \: at \: the \: design/known \: data \: point 
$$
or to interpolate the convective heat transfer coefficient based on data the user provides that 
relates the heat transfer coefficient to the operational mass flow rate and temperature. The
thermal and mechanical properties of the components in the model can be assumed constant or 
variation due to temperature can be accounted for given data provided in the parameter dialog box.
$$
k = f(T), \: Cp = f(T),\: \alpha = f(T), \: E = f(T), \: \nu = f(T)
$$
where
$$
T = temperature \: of \: the \: component
$$
$$
k = thermal \: conductivity
$$
$$
Cp = heat \: capacity
$$
$$
\alpha = thermal \: expansion \: coefficient
$$
$$
E = Young's Modulus
$$
$$
\nu = Poisson's Ratio
$$
<br>
<p>The thermal models of each of the components have the ability to run at different rates than 
each other and the simulation time-step outside of this block. However it is a constraint in Simulink 
that all time-steps must be multiples of the lowest time-step in the simulation.<p>
<p>If you want to start this block at a steady state initial condition then consider using the 
<a href="SSTipClearance.html">Steady-State Tip Clearance</a>
block to evaluate the intial temperatures and lengths at the initial engine operating state. The 
results from that block can be input into the parameter dialog box of this block in the proceeding 
simulation.<p>
<p>The main outputs of this block are the tip clearance and nominal tip clearance. The tip clearance
is the current gap between the tip of the blade and the inner surface of the shroud. The nominal
tip clearance refers to what that gap would be if the engine reached as steady-state tip clearance
with current instantaneous operating state. Other outputs include temperatures and lengths of the 
turbine components.<p>
<p>All inputs and parameters (masked variables) are in standard English units. The units are indicated 
in the tables below as well as the block cover and dialog box. Outputs are in standard English units 
with the exception of the tip clearance which is in mils (1mil = 0.001in).<p>
<br>
<font size="5" color="Blue">Dynamic Tip Clearance Inputs:</font>
<table border="1"> <tr><td>Tip Clearance Input</td><td>Description</td></tr>
    <tr><td>Nmech</td><td>shaft speed [rpm]</td></tr>
	<tr><td>Tcore - Blade</td><td>temperature of the flow inside the core that is exposed to the blade (neglecting film cooling) [degR]</td></tr>
	<tr><td>Wcore</td><td>mass flow rate of the flow inside the core [slug/sec]</td></tr>
	<tr><td>Tcool - Blade</td><td>temperature of the flow used for film cooling [degR]</td></tr>
	<tr><td>Tcool - Rotor Front</td><td>temperature of the flow used to cool the front of the rotor disc [degR]</td></tr>
	<tr><td>Wcool - Rotor Front</td><td>mass flow rate of the flow used to cool the front of the rotor disc [slug/sec]</td></tr>
	<tr><td>Tcool - Rotor Back</td><td>temperature of the flow used to cool the back of the rotor disc [degR]</td></tr>
	<tr><td>Wcool - Rotor Back</td><td>mass flow rate of the flow used to cool the back of the rotor disc [slug/sec]</td></tr>
	<tr><td>Tin - Case</td><td>temperature of the flow on the inner surface of the engine case [degR]</td></tr>
    <tr><td>Win - Case</td><td>mass flow rate of the flow used to cool the inner surface of the engine case [slug/sec]</td></tr>
    <tr><td>Tout - Case</td><td>temperature of the flow on the outer surface of the engine case [degR]</td></tr>
    <tr><td>Wout - Case</td><td>mass flow rate of the flow used to cool the outer surface of the engine case [slug/sec]</td></tr>
	<tr><td>Wout Nom - Case</td><td>nominal mass flow rate of the flow used to cool the outer surface of the engine case (defined by the nominal cooling schedule) [slug/sec]</td></tr>
</table>
<br>
<font size="5" color="Blue">Dynamic Tip Clearance Outputs:</font>
<table border="1"> <tr><td>Tip Clearance Output</td><td>Description</td></tr>
    <tr><td>Out</td><td>Tip Clearance Output, structure consisting of 1 variable and 3 substructions:
            <br>- TC - tip clearance [mils]
            <br>- TCnom - nominal tip clearance (considering nominal cooling) [mils]
            <br>- Case
			<br>---- T - array containing the temperature solution for the engine case [degR]
			<br>---- Tavg - average temperature of the engine case [degR]
			<br>---- L - inner radius of the case [ft]
            <br>---- Lnom - nominal inner radius of the case (considering nominal cooling) [ft]
			<br>- Blade
			<br>---- T - temperature of the blade [degR]
			<br>---- L - length of the blade [ft]
            <br>---- Lu - unstrained length of the blade (without considering centrifugal expansion) [ft]
            <br>---- Lnom - nominal length of the blade (considering nominal cooling) [ft]
			<br>- Rotor
			<br>---- T - array containing the temperature solution for the rotor disc [degR]
			<br>---- Tavg - average temperature of the rotor disc [degR]
			<br>---- L - outer radius of the rotor disc [ft] 
            <br>---- Lu - unstrained outer radius of the rotor disc (without considering centrifugal expansion) [ft]
            <br>---- Lnom - nominal outer radius of the rotor disc (considering nominal cooling) [ft]</td></tr>
</table>
<br>
<font size="5" color="Blue">Dynamic Tip Clearance Mask Variables: </font>
<table border="1"> <tr><td>Turbine Mask Variable</td><td>Description</td></tr>
	<tr><td>m_Blade_M</td><td>mass of the blade [slug]</td></tr>
	<tr><td>A_Blade_M</td><td>effective surface area of the blade [ft^2]</td></tr>
	<tr><td>Cp_TempDependence_Blade_M</td><td>temperature dependence of the heat capcity of the blade. When unchecked the constant heat capacity Cp_Blade_M is used and when checked the heat capacity is interpolated each time-step based on temperature and heat capacity data given by TCp_Blade_Data_M and Cp_Blade_Data_M</td></tr>
	<tr><td>Cp_Blade_M</td><td>constant heat capacity for the blade [Btu/(slug-R)]</td></tr>
	<tr><td>TCp_Blade_Data_M</td><td>temperature array for interpolating the heat capacity of the blade [degR] (ax1)</td></tr>
	<tr><td>Cp_Blade_Data_M</td><td>heat capacity array correspondeing to Tc_Blade_Data_M for interpolating the heat capacity of the blade [Btu/(slug-R)] (ax1)</td></tr>
	<tr><td>eta_Blade_M</td><td>film cooling coefficient for cooling of the blade [frac]</td></tr>
	<tr><td>T0_Blade_M</td><td>initial temperature of the blade [degR]</td></tr>
	<tr><td>dt_Blade_M</td><td>time-step for solving for the blade temperature state and sampling time of the blocks involved with this calculation [sec]</td></tr>
	<tr><td>h_Const_Blade_M</td><td>check to use the constant h_Blade_M as the convective heat transfer coefficient for the blade</td></tr>
	<tr><td>h_Eqn_Blade_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the blade</td></tr>
	<tr><td>h_Data_Blade_M</td><td>check to use the data arrays Wc_Blade_Data_M, Tc_Blade_Data_M, and h_Blade_Data_M to interpolate the convective heat transfer coefficient for the blade</td></tr>
	<tr><td>h_Blade_M</td><td> constant convective heat transfer coefficient for the blade [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Blade_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the blade [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Blade_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the blade [slug/sec]</td></tr>
	<tr><td>Tdes_Blade_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for the blade [degR]</td></tr>
	<tr><td>Wc_Blade_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the blade [-] (bx1)</td></tr>
	<tr><td>Tc_Blade_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the blade [-] (cx1) </td></tr>
	<tr><td>h_Blade_Data_M</td><td> Matrix of convective heat transfer coefficients for the blade  rows corresponding to Wc_Blade_Data_M and columns corresponding to Tc_Blade_Data_M [Btu/(sec-ft^2-degR)] (bxc)</td></tr>
	<tr><td>L_Blade_M</td><td>length of the blade [ft]</td></tr>
	<tr><td>rho_Blade_M</td><td>density of the blade [slug/ft^3]</td></tr>
	<tr><td>alpha_TempDependence_Blade_M</td><td>temperature dependence of the thermal expansion coefficient of the blade. When unchecked the constant thermal expansion coefficient alpha_Blade_M is used and when checked the thermal expansion coefficient is interpolated each time-step based on temperature and thermal expansion coefficient data given by Talpha_Blade_Data_M and alpha_Blade_Data_M</td></tr>
	<tr><td>alpha_Blade_M</td><td>constant thermal expansion coefficient for the blade [1/degR)]</td></tr>
	<tr><td>Talpha_Blade_Data_M</td><td>temperature array for interpolating the thermal expansion coefficient of the blade [degR] (dx1)</td></tr>
	<tr><td>alpha_Blade_Data_M</td><td>thermal expansion coefficient array correspondeing to Talpha_Blade_Data_M for interpolating the thermal expansion coefficient of the blade [1/degR] (dx1)</td></tr>
	<tr><td>E_TempDependence_Blade_M</td><td>temperature dependence of Young's Modulus of the blade. When unchecked the constant Young's Modulus E_Blade_M is used and when checked Young's Modulus is interpolated each time-step based on temperature and Young's Modulus data given by TE_Blade_Data_M and E_Blade_Data_M</td></tr>
	<tr><td>E_Blade_M</td><td>constant Young's Modulus for the blade [lbf/ft^2]</td></tr>
	<tr><td>TE_Blade_Data_M</td><td>temperature array for interpolating Young's Modulus of the blade [degR] (ex1)</td></tr>
	<tr><td>E_Blade_Data_M</td><td>Young's Modulus array correspondeing to TE_Blade_Data_M for interpolating Young's Modulus of the blade [lbf/ft^2] (ex1)</td></tr>
	<tr><td>W_Rotor_M</td><td>width of the rotor from front to back [ft]</td></tr>
	<tr><td>n_Rotor_M</td><td>number of nodes in the spatial discretization of the rotor</td></tr>
	<tr><td>T0_Rotor_M</td><td>initial temperatures array for the rotor [degR] (n_Rotor_Mx1)</td></tr>
	<tr><td>dt_Rotor_M</td><td>time-step for solving for the rotor temperature state and sampling time of the blocks involved with this calculation [sec]</td></tr>
	<tr><td>rho_Rotor_M</td><td>density of the rotor [slug/ft^3]</td></tr>
	<tr><td>k_TempDependence_Rotor_M</td><td>temperature dependence of the thermal conductivity of the rotor. When unchecked the constant thermal conductivity k_Rotor_M is used and when checked the thermal conductivity is interpolated each time-step based on temperature and thermal conductivity data given by Tk_Rotor_Data_M and k_Rotor_Data_M</td></tr>
	<tr><td>k_Rotor_M</td><td>constant thermal conductivity for the rotor [Btu/(sec-ft-degR)]</td></tr>
	<tr><td>Tk_Rotor_Data_M</td><td>temperature array for interpolating the thermal conductivity of the rotor [degR] (fx1)</td></tr>
	<tr><td>k_Rotor_Data_M</td><td>thermal conductivity array correspondeing to Tk_Rotor_Data_M for interpolating the thermal conductivity of the rotor [Btu/(sec-ft-degR)] (fx1)</td></tr>
	<tr><td>Cp_TempDependence_Rotor_M</td><td>temperature dependence of the heat capcity of the rotor. When unchecked the constant heat capacity Cp_Rotor_M is used and when checked the heat capacity is interpolated each time-step based on temperature and heat capacity data given by TCp_Rotor_Data_M and Cp_Rotor_Data_M</td></tr>
	<tr><td>Cp_Rotor_M</td><td>constant heat capacity for the rotor [Btu/(slug-R)]</td></tr>
	<tr><td>TCp_Rotor_Data_M</td><td>temperature array for interpolating the heat capacity of the rotor [degR] (gx1)</td></tr>
	<tr><td>Cp_Rotor_Data_M</td><td>heat capacity array correspondeing to Tc_Rotor_Data_M for interpolating the heat capacity of the rotor [Btu/(slug-R)] (gx1)</td></tr>
	<tr><td>h_Const_Rotor_Front_M</td><td>check to use the constant h_Rotor_Front_M as the convective heat transfer coefficient for the front surface of the rotor</td></tr>
	<tr><td>h_Eqn_Rotor_Front_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the front surface of the rotor</td></tr>
	<tr><td>h_Data_Rotor_Front_M</td><td>check to use the data arrays Wc_Rotor_Front_Data_M, Tc_Rotor_Front_Data_M, and h_Rotor_Front_Data_M to interpolate the convective heat transfer coefficient for the front surface of the rotor</td></tr>
	<tr><td>h_Rotor_Front_M</td><td> constant convective heat transfer coefficient for the front surface of the rotor [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Rotor_Front_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the front surface of the rotor [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Rotor_Front_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the front surface of the rotor [slug/sec]</td></tr>
	<tr><td>Tdes_Rotor_Front_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for the front surface of the rotor [degR]</td></tr>
	<tr><td>Wc_Rotor_Front_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the front surface of the rotor [-] (hx1)</td></tr>
	<tr><td>Tc_Rotor_Front_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the front surface of the rotor [-] (ix1) </td></tr>
	<tr><td>h_Rotor_Front_Data_M</td><td> Matrix of convective heat transfer coefficients for the front surface of the rotor with rows corresponding to Wc_Rotor_Front_Data_M and columns corresponding to Tc_Rotor_Front_Data_M [Btu/(sec-ft^2-degR)] (hxi)</td></tr>
	<tr><td>h_Const_Rotor_Back_M</td><td>check to use the constant h_Rotor_Front_M as the convective heat transfer coefficient for the back surface of the rotor</td></tr>
	<tr><td>h_Eqn_Rotor_Back_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the back surface of the rotor</td></tr>
	<tr><td>h_Data_Rotor_Back_M</td><td>check to use the data arrays Wc_Rotor_Front_Data_M, Tc_Rotor_Front_Data_M, and h_Rotor_Front_Data_M to interpolate the convective heat transfer coefficient for the back surface of the rotor</td></tr>
	<tr><td>h_Rotor_Back_M</td><td> constant convective heat transfer coefficient for the back surface of the rotor [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Rotor_Back_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the back surface of the rotor [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Rotor_Back_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the back surface of the rotor [slug/sec]</td></tr>
	<tr><td>Tdes_Rotor_Back_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for the back surface of the rotor [degR]</td></tr>
	<tr><td>Wc_Rotor_Back_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the back surface of the rotor [-] (jx1)</td></tr>
	<tr><td>Tc_Rotor_Back_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the back surface of the rotor [-] (kx1) </td></tr>
	<tr><td>h_Rotor_Back_Data_M</td><td> Matrix of convective heat transfer coefficients for the back surface of the rotor with rows corresponding to Wc_Rotor_Front_Data_M and columns corresponding to Tc_Rotor_Front_Data_M [Btu/(sec-ft^2-degR)] (jxk)</td></tr>
	<tr><td>Ro_Rotor_M</td><td>outer radius of the rotor [ft]</td></tr>
	<tr><td>alpha_TempDependence_Rotor_M</td><td>temperature dependence of the thermal expansion coefficient of the rotor. When unchecked the constant thermal expansion coefficient alpha_Rotor_M is used and when checked the thermal expansion coefficient is interpolated each time-step based on temperature and thermal expansion coefficient data given by Talpha_Rotor_Data_M and alpha_Rotor_Data_M</td></tr>
	<tr><td>alpha_Rotor_M</td><td>constant thermal expansion coefficient for the rotor [1/degR)]</td></tr>
	<tr><td>Talpha_Rotor_Data_M</td><td>temperature array for interpolating the thermal expansion coefficient of the rotor [degR] (lx1)</td></tr>
	<tr><td>alpha_Rotor_Data_M</td><td>thermal expansion coefficient array correspondeing to Talpha_Rotor_Data_M for interpolating the thermal expansion coefficient of the rotor [1/degR] (lx1)</td></tr>
	<tr><td>E_TempDependence_Rotor_M</td><td>temperature dependence of Young's Modulus of the rotor. When unchecked the constant Young's Modulus E_Rotor_M is used and when checked Young's Modulus is interpolated each time-step based on temperature and Young's Modulus data given by TE_Rotor_Data_M and E_Rotor_Data_M</td></tr>
	<tr><td>E_Rotor_M</td><td>constant Young's Modulus for the rotor [lbf/ft^2]</td></tr>
	<tr><td>TE_Rotor_Data_M</td><td>temperature array for interpolating Young's Modulus of the rotor [degR] (mx1)</td></tr>
	<tr><td>E_Rotor_Data_M</td><td>Young's Modulus array correspondeing to TE_Rotor_Data_M for interpolating Young's Modulus of the rotor [lbf/ft^2] (mx1)</td></tr>
	<tr><td>v_TempDependence_Rotor_M</td><td>temperature dependence of Poisson's ratio of the rotor. When unchecked the constant Poisson's ratio v_Rotor_M is used and when checked Poisson's ratio is interpolated each time-step based on temperature and Poisson's ratio data given by Tv_Rotor_Data_M and v_Rotor_Data_M</td></tr>
	<tr><td>v_Rotor_M</td><td>constant Young's Modulus for the rotor [-]</td></tr>
	<tr><td>Tv_Rotor_Data_M</td><td>temperature array for interpolating Poisson's ratio of the rotor [degR] (nx1)</td></tr>
	<tr><td>v_Rotor_Data_M</td><td>Poisson's ratio array correspondeing to Tv_Rotor_Data_M for interpolating Poisson's ratio of the rotor [-] (nx1)</td></tr>'
	<tr><td>W_Case_M</td><td>width of the engine case [ft]</td></tr>
	<tr><td>n_Case_M</td><td>number of nodes in the spatial discretization of the engine case</td></tr>
	<tr><td>T0_Case_M</td><td>initial temperatures array for the engine case [degR] (n_Case_Mx1)</td></tr>
    <tr><td>dt_Case_M</td><td>time-step for solving for the engine case temperature state and sampling time of the blocks involved with this calculation [sec]</td></tr>
    <tr><td>rho_Case_M</td><td>density of the engine case [slug/ft^3]</td></tr>
	<tr><td>k_TempDependence_Case_M</td><td>temperature dependence of the thermal conductivity of the engine case. When unchecked the constant thermal conductivity k_Case_M is used and when checked the thermal conductivity is interpolated each time-step based on temperature and thermal conductivity data given by Tk_Case_Data_M and k_Case_Data_M</td></tr>
	<tr><td>k_Case_M</td><td>constant thermal conductivity for the engine case [Btu/(sec-ft-degR)]</td></tr>
	<tr><td>Tk_Case_Data_M</td><td>temperature array for interpolating the thermal conductivity of the enigne case [degR] (ox1)</td></tr>
	<tr><td>k_Case_Data_M</td><td>thermal conductivity array correspondeing to Tk_Case_Data_M for interpolating the thermal conductivity of the engine case [Btu/(sec-ft-degR)] (ox1)</td></tr>
	<tr><td>Cp_TempDependence_Case_M</td><td>temperature dependence of the heat capcity of the engine case. When unchecked the constant heat capacity Cp_Case_M is used and when checked the heat capacity is interpolated each time-step based on temperature and heat capacity data given by TCp_Case_Data_M and Cp_Case_Data_M</td></tr>
	<tr><td>Cp_Case_M</td><td>constant heat capacity for the engine case [Btu/(slug-R)]</td></tr>
	<tr><td>TCp_Case_Data_M</td><td>temperature array for interpolating the heat capacity of the engine case [degR] (px1)</td></tr>
	<tr><td>Cp_Case_Data_M</td><td>heat capacity array correspondeing to Tc_Case_Data_M for interpolating the heat capacity of the engine case [Btu/(slug-R)] (px1)</td></tr>
	<tr><td>h_Const_Case_In_M</td><td>check to use the constant h_Case_In_M as the convective heat transfer coefficient for the inner surface of the engine case</td></tr>
	<tr><td>h_Eqn_Case_In_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the inner surface of the engine case</td></tr>
	<tr><td>h_Data_Case_In_M</td><td>check to use the data arrays Wc_Case_In_Data_M, Tc_Case_In_Data_M, and h_Case_In_Data_M to interpolate the convective heat transfer coefficient for the inner surface of the engine case</td></tr>
	<tr><td>h_Case_In_M</td><td> constant convective heat transfer coefficient for the inner surface of the engine case [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Case_In_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the inner surface of the engine case [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Case_In_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the inner surface of the engine case [slug/sec]</td></tr>
	<tr><td>Tdes_Case_In_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for inner surface of the engine case [degR]</td></tr>
	<tr><td>Wc_Case_In_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the inner surface of the engine case [-] (sx1)</td></tr>
	<tr><td>Tc_Case_In_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the inner surface of the engine case [-] (tx1) </td></tr>
	<tr><td>h_Case_In_Data_M</td><td> Matrix of convective heat transfer coefficients for the inner surface of the engine case with rows corresponding to Wc_Case_In_Data_M and columns corresponding to Tc_Case_In_Data_M [Btu/(sec-ft^2-degR)] (sxt)</td></tr>
	<tr><td>h_Const_Case_Out_M</td><td>check to use the constant h_Case_Out_M as the convective heat transfer coefficient for the outer surface of the engine case</td></tr>
	<tr><td>h_Eqn_Case_Out_M</td><td>check to use the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 to determine the convective heat transfer coefficient for the outer surface of the engine case</td></tr>
	<tr><td>h_Data_Case_Out_M</td><td>check to use the data arrays Wc_Case_Out_Data_M, Tc_Case_Out_Data_M, and h_Case_In_Data_M to interpolate the convective heat transfer coefficient for the outer surface of the engine case</td></tr>
	<tr><td>h_Case_Out_M</td><td> constant convective heat transfer coefficient for the outer surface of the engine case [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>hcoeff_Case_Out_M</td><td> coefficient in the equation h = hcoeff*(T/Tdes)^0.23*(W/Wdes)^0.8 used to evaluate the convective heat transfer coefficient for the outer surface of the engine case [Btu/(sec-ft^2-degR)]</td></tr>
	<tr><td>Wdes_Case_Out_M</td><td> mass flow rate at a design point (known point) used to normalize the mass flow rate in the convective heat transfer coefficient model for the outer surface of the engine case [slug/sec]</td></tr>
	<tr><td>Tdes_Case_Out_M</td><td> temperature at a design point (known point) used to normalize the temperature in the convective heat transfer coefficient model for outer surface of the engine case [degR]</td></tr>
	<tr><td>Wc_Case_Out_Data_M</td><td> Non-dimensional mass flow rate (W/Wdes) array used in interpolating the convective heat transfer coefficient for the outer surface of the engine case [-] (ux1)</td></tr>
	<tr><td>Tc_Case_Out_Data_M</td><td> Non-dimensional temperature (T/Tdes) array used in interpolating the convective heat transfer coefficient for the outer surface of the engine case [-] (vx1) </td></tr>
	<tr><td>h_Case_Out_Data_M</td><td> Matrix of convective heat transfer coefficients for the outer surface of the engine case with rows corresponding to Wc_Case_Out_Data_M and columns corresponding to Tc_Case_Out_Data_M [Btu/(sec-ft^2-degR)] (uxv)</td></tr>
	<tr><td>Ri_Case_M</td><td>inner radius of the structural layer of the engine case [ft]</td></tr>
	<tr><td>L_Shroud_M</td><td>Distance between the inner surface of the shroud and the inner surface of the engine case [ft]</td></tr>
    <tr><td>alpha_TempDependence_Case_M</td><td>temperature dependence of the thermal expansion coefficient of the structural layer of the engine case. When unchecked the constant thermal expansion coefficient alpha_Case_M is used and when checked the thermal expansion coefficient is interpolated each time-step based on temperature and thermal expansion coefficient data given by Talpha_Case_Data_M and alpha_Case_Data_M</td></tr>
	<tr><td>alpha_Case_M</td><td>constant thermal expansion coefficient for the engine case [1/degR)]</td></tr>
	<tr><td>Talpha_Case_Data_M</td><td>temperature array for interpolating the thermal expansion coefficient of the engine case [degR] (wx1)</td></tr>
	<tr><td>alpha_Case_Data_M</td><td>thermal expansion coefficient array correspondeing to Talpha_Case_Data_M for interpolating the thermal expansion coefficient of the engine case [1/degR] (wx1)</td></tr>
	<tr><td>dt_M</td><td>Time-step/sampling time of the simulation outside of the tip clearance block. It is used for properly transitioning rates within the block [sec]</td></tr>
	<tr><td>T0_Core_M</td><td>Initial temperature of the core flow (neglecting film cooling) [degR]</td></tr>
	<tr><td>W0_Core_M</td><td>Initial mass flow rate of the core flow [slug/sec]</td></tr>
	<tr><td>Tcool0_Blade_M</td><td>Initial temperature of the cooling flow for the blade [degR]</td></tr>
	<tr><td>Tcool0_Rotor_Front_M</td><td>Initial temperature of the cooling flow for the front of the rotor [degR]</td></tr>
	<tr><td>Wcool0_Rotor_Front_M</td><td>Initial mass flow rate of the cooling flow for the front of the rotor [slug/sec]</td></tr>
	<tr><td>Tcool0_Rotor_Back_M</td><td>Initial temperature of the cooling flow for the back of the rotor [degR]</td></tr>
	<tr><td>Wcool0_Rotor_Back_M</td><td>Initial mass flow rate of the cooling flow for the back of the rotor [slug/sec]</td></tr>
    <tr><td>Tcool0_Case_In_M</td><td>Initial temperature of the cooling flow for the inner surface of the engine case [degR]</td></tr>
	<tr><td>Wcool0_Case_In_M</td><td>Initial mass flow rate of the cooling flow for the inner surface of the engine case [slug/sec]</td></tr>
	<tr><td>Tcool0_Case_Out_M</td><td>Initial temperature of the cooling flow for the outer surface of the engine case [degR]</td></tr>
	<tr><td>Wcool0_Case_Out_M</td><td>Initial mass flow rate of the cooling flow for the outer surface of the engine case [slug/sec]</td></tr>
    <tr><td>Wcool0_Case_Out_M</td><td>Initial nominal mass flow rate of the cooling flow for the outer surface of the engine case (based on the nominal cooling schedule) [slug/sec]</td></tr>
</table>
<br>


